Question

Notation for hypothesis tests about a population mean

Suppose you are conducting a study about how the average US worker spends time over the course of a workday. You are interested in how much time workers spend per day on personal calls, emails, and social networking websites, as well as how much time they spend socializing with coworkers versus actually working.

The most recent census provides data for the entire population of US workers on variables such as travel time to work, time spent at work, and break time at work. The census, however, does not include data on the variables you are interested in, so you obtain a random sample of 50 full-time workers in the United States and ask about personal calls, emails, and so forth. You are curious about how your sample compares with the census, so you also ask the workers the same questions about work that are asked in the census.

Suppose the mean travel time to work from the most recent census is 20.6 minutes, with a standard deviation of 10.6 minutes. Your sample of 50 US workers provides a mean travel time to work of 23.6 minutes with a sample standard deviation of 8.3 minutes.

Organize this information by completing the following table.

Answer 1

Null hypothesis:

Ho:

Alternative hypothesis:

Ha:

alpha=0.05

z statistic is

z=xbar-mu/sigma/sqrt(n)

xbar---sample mean

mu---population mean

sigma ---population std dev

n----sample size

z=(23.6-20.6)/(10.6/sqrt(50)

z=2.001

z crit for 95%=1.96

Z stat >z crit

Reject null hypothesis and

Accept alternative hypothesis.

Conclusion:

There is no sufficient evidence at 5% level of significance to conclude that he average US worker spends time over the course of a workday is 20.6 minutes